BIPOLAR JUNCTION TRANSISTORS

Transcription

1 CHAPTER 3 BIPOLAR JUNCTION TRANSISTORS A bipolar junction transistor, BJT, is a single piece of silicon with two back-to-back P-N junctions. However, it cannot be made with two independent back-to-back diodes. BJTs can be made either as PNP or as NPN. The circuit symbols and representations of their configuration are given below. They have three regions and three terminals, emitter, base, and collector represented by E, B, and C respectively. The difference in the circuit symbols is the direction of the arrow. As we shall see shortly, the direction of the arrow indicates the direction of the current in the emitter when the transistor is conducting normally. As a way to remember which is which, a former student explained to me that NPN stands for "Not Pointing in". Figure 1. BJT symbols and representations In digital electronics applications, we are interested in using the transistor as a switch and will concentrate on switching characteristics, rather than the linear properties. We will start with an overview of the operation of the transistor. Because most bipolar switching circuits use NPN transistors, we shall concentrate primarily on them. There are four possible combinations, the base-collector junction may be either forward or reverse biased, and the base-emitter junction can also be biased either way. The four possibilities are shown in Figure 2 which also shows the operating region for each combination. Figure 2. The four operating conditions Bipolar Junction Transistors 1

2 The reverse active region is seldom used, but as we will see, it occurs in TTL gates. We begin our study of transistors by looking at each region of operation. Figure 3. Common Base Configuration Showing Biasing Arrangement for Cutoff CUTOFF REGION (Both junction reverse biased) Let us start with the cutoff region, both junctions reverse biased as shown in Figure 3. With reverse biasing, we can assume that all currents are zero. We know that there are leakage currents associated with reverse biased junctions, but these currents are small and will be ignored. Figure 4. Common base configuration with biasing for the forward active region FORWARD-ACTIVE REGION (BE junction forward biased, BC junction reverse biased) The biasing condition for the forward active region of operation is shown in the Figure 4. The BE junction is forward biased and the BC junction is reverse biased. In this case, the forward bias of the BE junction will cause the injection of both holes and electrons across the junction. The holes are of little consequence because the doping levels are adjusted to minimize the hole current. The electrons are the carriers of interest. The electrons are injected into the base region where they are called the minority carrier even though they greatly outnumber the holes. They "pile up" at the BE junction. From there they diffuse across the base region due to the concentration gradient. Some are lost due to holeelectron recombination, but the majority reach the BC junction. At the BC junction, the electrons encounter a potential gradient (due to the depletion region) and are swept across the junction into the collector region. Bipolar Junction Transistors 2

3 Figure 5. Common Base Configuration in forward Active region Showing Internal Currents As shown in Figure 5, there are several components of current: 1. Holes injected from B-E. This is small and is ignored. 2. Electrons injected from base to emitter. This is -I E 3. Electrons that reach the collector. This is -α F I E. 4. Recombination current. This is -(1 - α F )I E. 5. Collector reverse saturation current I C0, which we will usually neglect. The term α F is the forward current transfer ratio. This term refers to the fraction of electrons that reach the collector from those that are injected into the base region across the emitter junction. In most transistors, α F is close to unity, typically The difference between the current that is injected into the base region and that reaches the collector, becomes the base current. Thus, in most transistors, the base current is quite small, and the collector and emitter currents are close to the same magnitude. The sum of currents entering the three terminals must equal zero, I B + I C + I E = 0 (1) Also from current components 3 and 5 above, I C = -α F I E + I C0 (2) These two equations describe the currents in the common-base configuration in the forward-active region as shown in Fig. 5. We can go back to the cutoff region from here by reducing the bias voltage between base and emitter. Since the BE junction is just a P-N junction, this current is essentially a diode current. Reducing this bias voltage to zero will reduce the emitter current to zero. In this case, -I B = I C =I C0. We will hang on to this leakage current for a while yet before we completely drop it. Bipolar Junction Transistors 3

4 SATURATION REGION (Both junctions forward biased) In the active region, the collector current is proportional to the emitter current (plus the leakage current, I C0 ). This implies that the voltage bias across the base-collector junction is unimportant. But if we look again at Fig. 5, we see a resistor in series with the collector lead. If the current increases to a point that the voltage drop across the resistor plus the collector supply voltage begins to forward bias the collector junction, then holes will be injected into the collector region from the base. This hole current will counteract increases in electrons coming from the emitter, effectively limiting the transistor current. The base-collector voltage V BC at which this limiting effect begins is at about V BC =0.4 Volts, and becomes fully limiting at about 0.6 Volts. This region of operation is known as saturation. Please note that our terminology can get a little confusing. In this case, saturation refers to the circuit, not the transistor. The transistor could carry more current but the external circuit, the voltage source and resistor in the collector circuit, limits the current. REVERSE ACTIVE REGION (BE junction reverse biased, BC junction forward biased) In this case, the biasing arrangement is just the reverse of the forward active region. The collector junction is forward biased, while the emitter junction is reverse biased. The operation is just the same as the forward active region, except all voltage sources, and hence collector and emitter currents, are the reverse of the forward bias case. Another difference is that α F is replaced by α R. The equation corresponding to Eq. 2 is: I E = -α R I C + I E0 This configuration is rarely used because most transistors are doped selectively to give forward current transfer ratios very near unity, which automatically causes the reverse current transfer ratio to be very low. NOTE Please be aware that the above discussion and resulting equations are only approximations to the total operation of a transistor. A number of other phenomena are simultaneously occurring, but for typical applications, these phenomena cause only small errors in analysis. Such phenomena are: surface leakage currents, current due to holes injected from base into the emitter, hole-electron thermal generation, body resistance of the transistor, and avalanche multiplication. It is not our intention to study all effects in the transistor in this course, but to develop means to reduce the characteristics to simple, but appropriate models which will allow us to easily analyze transistor switching circuits. However, in the process of developing and using a model, an engineer must develop a feeling for when it is appropriate to use such a model and the limitations on the model. Bipolar Junction Transistors 4

5 COMMON BASE AMPLIFIER Before we go on to the common emitter configuration, we should take a few moments to observe how a transistor can be used as an amplifier. Again referring to Fig. 5, assume that V EE is increased by 1mV. This change in voltage would cause an increase in the current in the PN junction between the base and emitter. Most of this current would be reflected in an increase in the collector current. This change in collector current would manifest itself in a change in the voltage across the collector resistor, R C. Now if the collector resistor is much larger than the emitter resistor, we would see a large voltage gain. We will not pursue this path further as this topic is the subject of another course. a. Common Base b. Common Emitter c. Common Collector Figure 6. Basic Configurations and Biasing for the NPN Transistors COMMON EMITTER CONFIGURATION The common-emitter configuration is much more prevalent than the common base configuration, especially in digital or switching circuits. This configuration is shown in Figure 6 along with the common base and common collector configurations for comparison. The name comes from the fact that the emitter terminal is held at ground or "common". If loop equations are written for both the input and the output circuits, the two currents of interest will be the collector current, I C, and base current, I B. Equation 2, above, is written in terms of the emitter and collector currents. By substituting Equation 1 into Equation 2, we can solve for the collector current in terms of the base current, Where we have dropped the subscript on α, since we are assuming forward active region. It is convenient to define a new variable, Thus, Equation 3 becomes, The terms β or h fe relate a change in base current to a change in collector current, or current gain. If we ignore I CO, then the dc current gain, h FE, is the ratio of collector to base currents. β is used interchangeably for both ac and dc current gain. Many times we use β and h FE interchangeably. Bipolar Junction Transistors 5

6 CIRCUIT MODELS FOR A COMMON EMITTER TRANSISTOR. BASE-EMITTER CIRCUIT When we go back and look at Figure 6, we can see that the relationship between base current and base-emitter voltage is controlled by the I-V characteristic of the base-emitter PN junction. While there is some effect caused by the collector-emitter voltage, these effects are quite small and for the purposes of this course, will be neglected. (The course in linear electronics does not neglect this effect, which is often expressed in terms of r µ.) Thus, we can consider the base-emitter junction to operate just like a diode, and model it similarly. When talking about digital logic gates, we will assume that there will be no base current if the base-emitter voltage V BE is less than V BEγ = 0.50 Volts. We will also assume that if the base is driven heavily (into saturation), the base-emitter voltage V BE is equal to V BEsat = 0.80 Volts. Sometimes it is convenient to use an intermediate value of 0.7 volts when the transistor is in the active region. We will also use voltages of 50 mv higher for the ECL gates which are discussed later. Figure 4 shows the circuit models we will use for the three regions of operation for the NPN transistor in the common emitter configuration. The base-emitter voltages are shown as discussed. Next we will. develop the collector models. Figure 7. Common Emitter Circuit Models for an NPN Transistor COLLECTOR EMITTER CIRCUIT MODELS The collector emitter circuit is more complex to model. Again we will talk about the three regions of operation. The collector characteristic is a plot of I C vs V CE for a few representative values of base current. Typical collector characteristics are given in Figures 8 and 9; the forward characteristic in Figure 8 and the reverse characteristic in Figure 9. Because the reverse active region is seldom used, we will not develop that model here. Bipolar Junction Transistors 6

7 Figure 8. Forward collector characteristics for a 2N3903 Bipolar Junction Transistors 7

8 Figure 9. Reverse characteristics for a 2N3903 Bipolar Junction Transistors 8

9 Cutoff If the base-emitter voltage is less than cut-in,v BEγ, the base current is zero. From Equation 3, we see that the only current is the leakage current which we usually consider negligible. Thus, we can consider the transistor in cutoff to be an open circuit between the three terminals as shown in Figure 7a. The limit is, of course, that V BE < 0.50 Volts. Active Region The discussion of the active and saturation regions rests on Equation 5 and the collector characteristic graph which is shown in Figure 8. The cutoff region is shown on the collector characteristic as the single line where the base current is zero; in this case the x- axis or I C =0. The active region is the large middle part of the family of curves where the collector current is essentially constant for a fixed base current. The saturation region is the left-hand portion of the curves where the curves are almost vertical. The curves in the active region correspond closely to Equation 5. The current is only a function of base current, not a function of collector-emitter voltage, V CE. In this case, a suitable model of the transistor is shown in Figure 7b. This figure shows the base-emitter model as a voltage source and the collector-emitter model as a current-controlled current source, βi B. The defining limitations are I B >0 and V CE >0.2 V. Again, you should be aware that this model is only an approximation to the real device. For instance, collector current does vary slightly with V CE and the spacing between the curves is not exactly constant; β varies somewhat with collector current. The course in linear electronics more closely models the first of these effects with an additional parameter, r o. Saturation Region The saturation region model is perhaps the poorest approximation to the real device. The saturation region is modeled simply as a fixed voltage of V CE = 0.2 Volts. In this region of operation, the base circuit is modeled as V BE = 0.80 Volts. This model is shown in Figure 4c. The limitations are that I B >0 and I C <βi B. From the curves in Figure 8, there is a substantial portion of the curve between the straight-line portions in the linear region to the nearly vertical lines in the saturation region. Probably the best way to view this transition is that β is decreasing. A typical approach is to assume that when one is discussing saturation, the appropriate β is approximately 85% that for the linear region. In this course, we will consider this problem in two ways. First, when we are working with problems in the early part of the course where we are considering operation in all three regions, we will assume β to be the linear β for all regions. Here we will assume that saturation is reached abruptly. In the Bipolar Junction Transistors 9

10 second case, when we are considering only cutoff and saturation regions, we will use a saturation β only. We will simply ignore the linear region. The models we use in both cases are the same and should cause little difficulty. CONCLUSION The effect of using the models for the three regions can be seen in Figure 10. In this figure, the cutoff region is represented by the straight line on the voltage axis, indicating zero current. The linear region is represented by a series of evenly spaced horizontal lines. The saturation region is represented by the vertical line at V CE =0.2 Volts. A comparison between Figures 8 and 10 will show that our models are only approximations to the actual characteristic. These approximations will, however, allow us to greatly simplify circuit analysis for the switching circuits in this course. These approximations will give us reasonably accurate solutions to these circuits. They will also be a great help to us when we attempt to understand circuit operation. Figure 10. A composite characteristic represented by the circuit models. Bipolar Junction Transistors 10

11 THE TRANSISTOR AS AN INVERTER/SWITCH The utility of a BJT in digital circuits is the ability of the transistor to block or conduct current with just a small control current. Thus, we are primarily interested in the cutoff and saturation modes of operation. In this section, we will discuss the transistor used both as a switch and as a linear inverter. We will use the circuit models of the transistor developed in the previous section. To start the discussion, we will consider the circuit in Figure 11. This circuit is the classic switch. The operation of the transistor is controlled by the current in the base circuit. Thus, the input voltage controls the circuit. We will analyze the circuit for three cases: V in =0, 5, and 10 Volts. Figure 11. Transistor Switch. Simplified Drawing. V in = 0 Because the base-emitter junction is a diode, this part of the circuit can be analyzed as we did earlier for diode circuits. With no source voltage to overcome the turn-on voltage of the diode, there will be no current flow. With no base current, the transistor is cutoff and there will be no collector current. See the circuit in Figure 12 where the transistor has been replaced with its cutoff model. With no current in the collector circuit, there will be zero voltage drop across the collector resistor. Hence the voltage between the collector and emitter will be V CE = V O = V CC = 10 Volts. (1) (Note the order of the subscripts, CE. A positive voltage for V CE means that the collector is more positive than the emitter.) Figure 12. Circuit With V in = 0. The transistor is replaced with its cutoff model. Bipolar Junction Transistors 11

12 V in = 5 Volts Figure 13. Circuit With V in = 5 Volts An analysis of the base circuit in this case indicates that the base current is not zero. From Figure 13, Since there is base current, there must be collector current. If we assume the transistor is in the active region, the active circuit model has replaced the transistor in Figure 13. We can solve this circuit for the collector current. I C = βi B = 20* 0.86 = 17.2 ma (3) The final information we would like to know is the output voltage, the voltage at the collector. We cannot get V CE directly, we have to use the voltage drop across the collector resistor; V O = V CE = V CC - I C R C = ma* KΩ = 1.4 V (4) Since V CE >V CEsat (=0.2V), this result is consistent with the assumption that the transistor is operating in the active region. Now let us look at the final case. V in = 10 Volts If we assume the transistor will be in the active region, the process will be the same as for the previous case. We can look at Figure 13 but with the input voltage at 10 volts. Proceeding to the collector circuit, we will attempt to find the collector current as we did before; I C = βi B = 20 * 1.86 = 37.2 ma (6) The output voltage is then, Bipolar Junction Transistors 12

13 V O = V CC - I R = *.500 = Volts?? (7) This result says that the output voltage is negative. How can that possibly be? There is no source for the negative voltage; no negative power supply. The transistor is modeled as a current-controlled current source, but is not a current generator. It can only work within the limits of the power supplies. You will note on the collector characteristic curves that the collector voltage cannot go negative with a positive collector current. The obvious conclusion is that the transistor circuit has saturated, and the active region model is no longer valid. Figure 14. Circuit in Saturation If we go to the saturation region model, the circuit is shown in Figure 14. Note that the only base circuit change is to change V BE to 0.80 volts. This change makes the base current We can also determine the collector current, We already know that the output voltage is 0.2 Volts (=V CEsat) since the transistor is in saturation. The only thing left is to verify that the model used is appropriate for the situation. (We already know the active region model is inappropriate, and that we are not in cutoff, I B >0.) To demonstrate that the saturation model is appropriate, we need only show the I Csat <βi B. Since βi B = 36.8 ma > 19.6, the saturation model is appropriate. SUMMARY It is appropriate at this time to explicitly define the criteria for operation in each mode. Cutoff: V BE < V BEγ and V BC < V BCγ If this condition occurs, the base current will be zero and the collector current will be zero. Of course, we are ignoring the leakage currents. We are also not considering the possibility of using the transistor backwards with collector and emitter reversed. Thus, we are assuming that the collector voltage is more positive than the base voltage. We will discuss the value of V BEγ later. Active Region I B > 0, V BE = 0.70, I C = βi B, V CE > 0.2 V. Bipolar Junction Transistors 13

14 Saturation Region: I B > 0, V BE = 0.80, V CE = 0.2, I C < βi B. The value of V BEγ we choose will have a significant bearing on how we view the transition between cutoff and the active region. For logic systems, we will use V BEγ = 0.50 Volts. This is the value the base-emitter voltage must be less than to guarantee the transistor is cutoff. Note that when the transistor is saturated, V BE =0.80. For logic systems, any value in between is indeterminate. This inconsistency will not cause us any trouble in logic systems. However, this discrepancy will cause some difficulty when we are trying to find the transition between cutoff and active operation and between active and saturation operation. For our next example, we will discuss a transistor as an inverting amplifier that varies continuously between cutoff and saturation. INVERTING AMPLIFIER To get a better feel for how a transistor works with real signals, we will discuss a transistor inverter with a sine wave input. The transistor will operate in all three modes. The circuit is shown in Figure 15. Temporarily, we will assume V BEγ = 0.75 = V BEact = V BEsat In other words, there is no discontinuity from cutoff to the active region, and no discontinuity from the active region to saturation. Where do we start the analysis of such a circuit? First let us consider the possibilities. At any given instant of time, the transistor will either be cutoff, in active region, or saturated. From our previous example, we should note that if the input voltage is below a certain value, the transistor will be cutoff; above that value, the transistor will be in the active region with positive base current, and with the input voltage higher still, we get enough base current to saturate the transistor. Our job here is to determine which region or regions are utilized. First, let us look to see if the transistor is cutoff. Model: V BEγ = V BEactive = V BEsat =0.75 V CEsat = 0.2 Figure 15. Transistor Inverting Amplifier β = 40 Cutoff Bipolar Junction Transistors 14

15 In order for the transistor to conduct at all, the input voltage must be above V BEγ. Conversely, if the input voltage is below V BEγ, the transistor will be cutoff. Does that occur here? Yes, the input voltage may go as low as -5 Volts. Thus, for all the time the input voltage is below V BE =0.75 Volts, the transistor is cutoff. The transistor is replaced by its cutoff model in Figure 16. What then is the output voltage during this time? Since there is zero collector current, zero current through the collector resistor, there is zero voltage drop across the resistor, and the output voltage is V O = V CC = 10 Volts. (10) Figure 16 shows the circuit with the transistor replaced with its cutoff model and Figure 17 shows the input and output waveforms during the cutoff period. Figure 16. Circuit With Transistor Cutoff Figure 17. V o When Transistor is cutoff Active Region Figure 18. Transistor Inverter Circuit During Active Region If the input voltage goes above 0.75 V, the transistor goes into the active region. If we use the active model for the transistor and place it into the circuit as shown in Figure 18, we can then analyze the circuit. The base current is Thus, the base current will have a sinusoidal component like the input voltage, only shifted. Note that this equation is valid only if V in >V BEγ. The next question, of course, Bipolar Junction Transistors 15

16 is what is the output voltage? Since the collector current is βi B = 40I B, the output voltage is the supply voltage minus the drop across the collector resistor. Again, the output voltage has a sinusoidal component. This equation is valid only for V in >0.75 Volts, and also as long as the circuit is not saturated, V o = V CE >0.2 v. Thus, the output voltage is sinusoidal only for a portion of the cycle. It should also be noted that if the input voltage = 0.75 Volts, the output is equal to 10 Volts, which is consistent with the cutoff case, no discontinuity. We now need to determine if the circuit saturates. Saturation We note from our earlier example that the circuit will be in saturation if the collectoremitter voltage drops to 0.2 Volts. We could solve Equation 12 to find what input voltage would cause this to happen. However, we will take a more straightforward approach. Let us simply look at the saturation model for the circuit to determine what the input voltage must be in order to reach saturation. Figure 19. Transistor Inverter Circuit in Saturation The saturation model for the circuit is shown in Figure 19. We now work backwards from the collector circuit. In Figure 19, the collector current is The minimum base current required to support this collector current is The minimum input voltage required to furnish this much base current is V insatmin = V BEsat + I Bsat* R B = ma *10 KΩ = 3.2 Volts. (15) Bipolar Junction Transistors 16

17 Since the input voltage rises above this value, the circuit does indeed saturate and will be in saturation whenever V in >3.2 volts. In saturation, the output voltage is 0.2 Volts. Thus, Figure 20 shows the output voltage for the entire cycle. Figure 20 shows that the circuit spends relatively little time in the active region. However, during this time the output voltage has a sinusoidal component and that sinusoidal part has a negative sign with respect to the input voltage, hence, the name of inverter. Actually this circuit is not really suitable for a linear signal inverter without substantial modifications. The linear inverting amplifier is discussed in more detail in the linear electronics course. It is useful to note, however, that the circuit we have analyzed does "square up" a sine wave, making the signal useful for digital switching. Figure 20. Waveforms for a complete cycle for the inverting amplifier circuit. Voltage Transfer Characteristic It is often useful to plot the relationship between the output voltage and the input voltage, called the voltage transfer characteristic or VTC. For the previous example, we already know the transistor is cutoff for V in < 0.75 making V OCutoff = 10 and the transistor is in the active region when 0.75 < V in < 3.2. We also know the transistor is in saturation when V in > 3.2 making the V Osat = 0.2. In active region: V Oact = 10-4(V in ) = 13-4V in which is an equation for a straight line. The voltage transfer characteristic curve is shown in Figure 21. Bipolar Junction Transistors 17

18 Figure 21. Voltage transfer characteristic for the transistor inverter PNP Transistors The PNP transistor works the same as the NPN, except that the carriers are holes instead of electrons, and all the currents and voltages are in the opposite direction. Figure 22. PNP transistor with internal currents. Figure 22 is a drawing of a PNP transistor showing the internal and external currents. The internal currents correspond to the same currents as for the NPN transistor shown earlier. The currents of importance are numbered 2, 3, and 4, hole currents, injected from emitter to base(#2), the diffusion current that reaches the collector (#3), and the holes lost by recombination in the base region (#4). Currents #1, and #5, are parasitic and usually ignored. Because the external currents are considered positive going into a terminal by convention, I E = current #2 I C = - current #3 = -αi E I B = - current #4 = -(1-α)I E Bipolar Junction Transistors 18

19 The above equations relate the base and collector curents to the emitter currents as is usual for the common base configuration. However, because we usually use the transistors in the common emitter configuration, it is more convenient to reperesent the currents in terms of the base curents. We still get I C = βi B but now, I B is a negative quantity. We also still have I C + I B + I E = 0 making I E = I B + I C Now however, I E will be a positive quantity, and I B and I C are negative quantities. The currents in the PNP transistor are in the opposite direction as for the NPN transistor, making the voltage drops across the junctions in the opposite direction. Thus, for the PNP transistor operating in the active or saturated regions,v BE and V CE are negative values. A typical common emitter configuration is given in Figure 23. From the circuit model, I B = -1.3/5K = 0.26 ma The collector current is (β = 10) I C = -0.26β = -2.6 ma and the voltage at the collector is V O = K x 2.6 ma = -2.4 volts. Figure 23. Typical common emitter application for a PNP transistor with its active model. The difficulty in dealing with the PNP transistor is keeping track of the negative currents. Because most logic systems use positive voltages and because it is more intuitive to have currents going downhill instead of going uphill as in the above example, circuits can be drawn as shown in the application in Figure 24 as an output interface in a logic system.. Figure 24. PNP application in a logic system interface Bipolar Junction Transistors 19

20 In this case, we will assume the logic gate output is either +5 volts, or 0 volts. (Later on, we will use more accurate data for the gate.) If the gate output is high at +5, the voltage across the base-emitter junction is zero volts, which will keep the transistor cutoff. The circuit with its cutoff model is shown in Figure 25. Note that we specify the emitter-base voltage as V EB. In this case, V EB = 0, because both terminals are connected to +5 volts. Figure 25. Cutoff model Figure 26. Saturation model If the gate output is low, or zero volts, the emitter-base junction is turned on. We suspect the transistor is saturated, so we use the saturation model in Figure 26 for the analysis. It is convenient to use positive currents I 1 (= - I B ) and I 2 ( = - I C ) instead of their negative counterparts. Note again, we use reverse polarities for the the two terminal voltages. We can calculate the two currents I 1 = (5-0.8)/5K = 0.84 ma I 2 = (5-0.2)/1K = 4.8 ma If β = 10, the transistor is obviously in saturation, and V O = 4.8 volts. Notice that the voltage across the 1K load resistor is 4.8 volts. Bipolar Junction Transistors 20

21 EXERCISES 1. For the following circuit, assume the following model for the transistor: V BEγ = 0.5 v, V BEact = 0.7 v, V BEsat = 0.8 v, β = 30, V CEsat = 0.2 v. Circuit Diagram Voltage Transfer Characteristic If V in = 5.0 volts, a. Draw arrows showing the actual current direction in each terminal of the transistor. b. Determine three terminal currents: I B = I C = I E = c. Determine V o. V o = d. Find minimumv insat and maximum V incutoff. We can use these points to draw the voltage transfer characteristic, but because we are using a discontinuous transistor model, we cannot precisely predict the region in between. Simply draw a dotted line between the two points. 2. A ramp voltage is applied to the inverter circuit shown. A continuous model for the transistor is: V BEγ = V BEact = V BEsat = 0.7 volts V CEsat = 0.2 volts β = 25 Plot the output voltage waveform and determine the time it takes the output voltage to go from cutoff to saturation. 3. A PNP transistor circuit is shown below. The transistor model is: Bipolar Junction Transistors 21

22 V BEγ = V BEact = V BEsat = -0.70, V CEsat = -0.20, β = 20 If V in = 5.0 volts, a. Draw arrows showing the actual current direction in each terminal of the transistor. b. Determine three terminal currents: I B = I C = I E = c. Determine V o. V o = d. Find V insat and V incutoff. V insat = V incutoff = e. Draw the voltage transfer characteristic. Bipolar Junction Transistors 22

23 DESIGN EXAMPLE: TRANSISTOR SWITCH To illustrate the utility of a transistor as a switch, let's look at the following example. We have a signal from a 74HC00 CMOS logic gate that is supposed to turn on an LED when the output of the gate is a high. The specifications of interest are: 74HC00: V OHmin = 3.84 volts when I OH = ma, V OL = 0 at I OL = 0 LED: V D = 1.80 volts when I D =30 ma, I max = 60 ma Because we want the LED current to be about 30 ma, the logic gate clearly will not supply the necessary current. A BJT switch is a good candidate for this job. A suggested circuit is shown below. In this case, when the output of the gate is high, we want the transistor to saturate with 30 ma through the diode. When the output of the gate is low, the transistor will be turned off. The high output case is shown. Figure 27. Circuit to be designed First, let's look at the case when the gate output is low. In this case, the output voltage is zero and the transistor will be cutoff. There will also be no diode current. When the gate output is high as shown in the circuit above, we want the transistor to be saturated. If the diode current is 30 ma, and the diode voltage is 1.80 volts, the voltage across the series (current limiting) resistor, R c, is 3.0 volts. Thus, this resistor value must be 100 Ω. Assuming the transistor β sat =10, the base current must be greater than 3 ma to guarantee saturation. In this case, the gate can source 4 ma when the output voltage drops as low as 3.84 volts. If the base-emitter voltage is 0.8 volts, the voltage across the resistor must be 3.04 volts. At a base current of 4 ma, the resistor value is 760 Ω. Note that the base current in saturation needs only to be 3 ma or greater. Thus, the base resistor can be made larger, up to 1013 Ω. The standard 5% values between these limits are 820, 910, and 1000 Ω. Any of these values is satisfactory if we consider only nominal calculations. (If we must guarantee operation with 5% resistors, 800 < R NOM < 964.) With this design, the LED will be off when the gate output is low and the LED will be on when the gate output is high. Bipolar Junction Transistors 23

24 Problems 1. In the laboratory, take a set of transistor characteristic curves for a transistor in the forward active region. From these curves, develop the approximate, straight-line models for the three regions of operation. Present your results by drawing the circuit models with component values and by drawing the characteristic "curves" represented by these circuit models. Turn in the original collector characteristic curves, the circuit models, and the curves represented by these models. 2. For the circuit below, determine the values of the input voltages that will cause the transistor to be cutoff and saturated. Use the following model component values: β=50, V BEγ =0.50, V BEsat = 0.80, V CEsat = Problem 2 Problems 3 and 4 For Problems 3 and 4, use the following model for the transistor: β = 30, V BEγ = V BEact = V BEsat = 0.70, V CEsat = Draw the voltage transfer characteristic (V o vs V in ) for the circuit given. Let V in go high enough for the circuit to saturate. 4. Let the input voltage be a 5 volt sine wave (5sinωt). Sketch the output waveform showing all breakpoints in the waveform and the input voltage at each breakpoint. Determine the time it takes the output waveform go from one "rail" to the other if the frequency is 60 Hz. 5. Use a computer simulation to verify the results from Problem #4. Use the library model for a 2N3903 with Beta = 30. Note that the results may not be quite the same because the PSPICE library model is different from the 3-region model we use in class and that model includes capacitance. Be sure to show on your plots the time it takes to make the transition from cutoff to saturation. 6. Find the input voltage required to cause the pnp transistor circuit to saturate. Bipolar Junction Transistors 24

25 PNP Transistor Model: V EBsat = 0.8, V ECsat = 0.2, Beta sat = 20 Problem 6 7. The input voltage waveform is shown. Draw the output voltage waveform showing the input and output voltages at each breakpoint. The transistor has the following model parameters: V BEcutin = V BEact = V BEsat = 0.7 volts, V CEsat = 0.2 volts, Beta = A PNP transistor is used in the following circuit to drive a load as shown. Determine the value of the base resistor needed to guarantee saturation if the input voltage switches between +12 volts and 0.4 volts. Note that in one state, the pnp transistor will be cutoff and in the other state, the pnp transistor is to be saturated. The pnp transistor has the following model parameters: V EBcutin = 0.5 volts, V EBsat = 0.8 volts, V ECsat = 0.2 volts, Beta = 20 Bipolar Junction Transistors 25

26 Problem A Darlington connection is shown below. If 0.1 ma is going into the base of the first transistor, how much current can go through the resistor? Beta is 20 for each transistor. What is V CE for the output transistor? Bipolar Junction Transistors 26